Modeling and Phase Control of Phi-Bits in Coupled Acoustic Waveguides: A Classical Analogue to Qubits

Classical systems capable of mimicking quantum behavior offer a robust alternative for exploring information processing. Here, we present a validated theoretical framework for understanding phi-bits—nonlinear, phase-defined modes that act as classical analogues of qubits—in a system of three coupled, finite-length acoustic waveguides. Using a discrete mass–spring model, we reproduce the experimentally observed continuous phase evolution of low-order combination modes under dual-frequency excitation. The model incorporates end-spring nonlinearities, damping, and boundary constraints, capturing how phi-bit phases evolve with changing drive frequency. For spectrally isolated, high-SNR modes, the phase responses—predicted by linear combinations of the drivers’ phases—qualitatively match experimental results. We also assess the impact of higher-order nonlinearities, which extend accessible behaviors but can disrupt linearity unless spring coefficients are recalibrated via nondimensional scaling. This framework offers design criteria for selecting stable phi-bits, tuning sweep protocols, and porting models across geometries and materials. Our findings show that classical nonlinear lattices can emulate key aspects of quantum information flow, providing a tunable and predictive platform for phase-encoded logic and quantum-inspired acoustic computation.